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\[ f(t,X_t) = f(0,X_{0}) + \int_0^t \mu_s\frac{\partial f}{\partial t}(s,X_s) + \frac{\partial f}{\partial x}(s,X_s) + \frac{1}{2}\sigma^2_s\frac{\partial^2 f}{\partial x^2}(s,X_s) d s + \int_0^t \sigma_s\frac{\partial f}{\partial x}(s,X_s) d W_s \]

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last update on April 03 2016, by Pedro Baltazar